1. Field of the Invention
This invention relates to the field of superplastic forming and, more particularly, to the forming of objects from metallic alloys which exhibit superplastic characteristics when heated to particular temperature ranges.
2. Description of the Prior Art
Certain metallic alloys will exhibit superplasticity when heated to known temperature ranges. This characteristic is used to form objects from such alloys by placing a metallic alloy blank in a forming die containing a die cavity, heating the blank to the desired temperature, and then applying a pressure differential to the blank for a period of time. The pressure differential, also known as the forming pressure, is obtained by introducing a pressurized inert gas into the die cavity on one side of the blank while the cavity on the other side of the blank contains inert gas fluidly communicating with the ambient atmosphere, and thus remains at atmospheric pressure. The forming pressure forms the heated blank to the shape of the die cavity or to the shape of a male die located in the die cavity.
Forming pressure and strain rate are related variables. A forming schedule, also called a pressure forming cycle, provides the forming pressure as a function of time. Although there are different ways of deriving such a forming cycle, it is typically calculated by assuming that the strain rate remains constant during the forming cycle at a value that will not cause rupture, yet is high enough to achieve the desired forming within a reasonable period.
The forming pressure, P, is a function of the forming stress, .sigma., instantaneous thickness, T, and instantaneous radius of curvature, R, of the forming blank. This relationship can be expressed as EQU P=f.sub.1 (.sigma.,T,R)
The thickness, T, and radius or curvature, R, are functions of a forming progress parameter, h. Thus, the forming pressure can be expressed as EQU P=f.sub.2 (.sigma.,h)
The time, t, required for the blank to strain to a particular thickness, T, is a function of the thickness, T, and strain rate, .epsilon.: EQU t=g.sub.1 (T,.epsilon.)
Since the thickness, T, is a function of the forming progress parameter, h, the equation for time, t, can also be written as EQU t=g.sub.2 (h,.epsilon.)
Solving the foregoing equation for the forming progress parameter, h: EQU h=j(t,.epsilon.)
Substituting the foregoing expression for the forming progress parameter, h, into the latter equation for the forming pressure, P, provides the following equation: EQU P=f.sub.3 (.sigma.,t,.epsilon.)
The forming stress, .sigma., is a function of the strain rate, .epsilon.. The relationship between these two variables is empirically known for most metallic alloys, or can be obtained from a forming test. When the strain rate, .epsilon., is chosen for constant strain rate forming, the stress, .sigma., can thus be determined and is also assumed to be a constant. Thus, as these two variables are assumed to be constants, the equation for forming pressure, P, simplifies to one where the forming pressure, P, can be expressed solely as a function of time, t: EQU P=f.sub.4 (t)
A plot of forming pressure, P, versus time, t, can be generated from this equation, bearing in mind that this is the forming pressure required to maintain the constant value of strain rate, .epsilon., that was initially chosen.
An example of the foregoing type of approach is provided in U.S. Pat. No. 4,233,829 by Hamilton et al. As can be seen, the calculations necessary to produce the forming pressure versus time plot are complex and very time consuming, even for the simple geometry of a rectangular pan.
Hamilton et al further disclose apparatus for automatically supplying the forming pressure called for by the pressure versus time plot to the die cavity. Others, using similar methods of mathematical analysis, also have produced pressure versus time plots and then used other means to adjust the forming pressure with time in accordance with their pressure plots.
The problem inherent to the foregoing approaches is that any mathematical model used to obtain a plot of forming pressure versus time is only an approximation because the assumed value for the strain rate used in the model cannot be determined with any degree of certainty. A further critical assumption is that the strain rate remains constant whereas, in fact, it varies during the forming cycle.
The foregoing approaches also assume that the strain rate is the same over the entire surface of the blank, whereas it actually varies from point to point over the blank due to the blank's varying geometry during forming, variations in thickness, and temperature gradients. Another factor contributing to inaccuracy is that the superplasticity for the metallic alloy will vary among blanks composed of the same alloy due to innate variations in the production process.
The problems inherent to using a pressure versus time plot in superplastic forming are best explained by means of the example shown in FIGS. 1 and 2. FIG. 1 shows the superplastic forming of a deep cup in a deep cylindrical die cavity. A deep cup has a ratio of its depth to its radius that is greater than one. FIG. 2 is a graph of the actual forming pressure as a function of time for the superplastic forming of the deep cup shown in FIG. 1. The strain rate was kept as near as possible to a constant value.
To better understand FIGS. 1 and 2, one must bear in mind that as the blank strains, its radius of curvature decreases and, with the decreased radius, the forming pressure required to maintain a constant strain rate increases; and as the blank strains it thins, and with this thinning the forming pressure required to obtain a constant strain rate decreases. Initially, the blank is flat, thus having an infinite radius. This beginning position is shown in both figures as point 0. As the forming begins, the blank thins and spherically expands to a slight radius, as indicated by point 1. Through point 1 the radius is decreasing at a rate greater than the rate that the thickness is decreasing, and thus the forming pressure required to maintain a constant strain rate is increasing.
Through point 2 the radius continues to decrease at a rate greater than the thickness is decreasing, and so the required forming pressure continues to increase. At point 3 the blank forms a hemisphere. From point 3 to point 4, where the center of the blank first touches the bottom of the die cavity, the radius remains constant. As the thickness of the blank continues to decrease, the required pressure also decreases. The pressure thus reaches a local maximum at point 3, and steadily decreases thereafter until reaching point 4.
After contacting the bottom of the die cavity, the blank begins to form into the corner of the die cavity, with the result that the radius again decreases at a greater rate than the thinning of the thickness. The required pressure thus forms a local minimum at point 4, and thereafter increases as the corner is being formed at point 5. The pressure continues to increase until the corner is formed against the die radius at point 6 and the forming cycle ends.
As previously discussed, the forming pressure is typically regulated according to a pressure versus time plot derived by attempting to achieve a constant strain rate and applying the methodology of the prior art. There are two modes which may lead to excessive strain resulting in rupture of the blank: fast forming and slow forming.
In the former, the blank expands faster than anticipated due to the combined inaccuracies inherent to the methodology of the prior art that have been previously discussed. The blank thus enters the constant radius zone between points 3 and 4 of FIG. 1 before anticipated and thus during the period when, although the required pressure is decreasing, the pressure being applied pursuant to the pressure versus time plot is being increased until the local maximum is reached at point 3 of FIG. 2. The applied pressure thus becomes progressively higher than the pressure necessary to produce the desired constant strain rate, resulting in a strain rate which may exceed the rate that the blank can withstand.
In the extreme case, the blank may have a strain rate so high that it ruptures even before it reaches point 3 of FIG. 1.
If rupture has not occurred by time point 3 is reached on the pressure versus time plot of FIG. 2, the differential between the applied pressure and the pressure necessary to produce the desired constant strain rate will continue to widen, albeit at a lower rate, because the higher than anticipated strain rate will cause thinning to occur at a greater rate than would normally be the case, thus further reducing the required pressure and concomitantly increasing the strain rate. Rupture may occur at any time until the blank touches the bottom of the cavity and the required pressure begins to increase.
The slow forming mode occurs when the blank forms slower than anticipated. The local maximum for the applied forming pressure occurring at point 3 of FIG. 2 thus occurs before the blank actually reaches point 3 in FIG. 1. The pressure is thus decreased early, before the blank enters the constant radius zone between points 3 and 4 of FIG. 1. The result is that the forming lags even further behind the positions anticipated by the pressure versus time plot of FIG. 2.
The problem occurs when the pressure versus time plot reaches point 4 and the pressure is rapidly increased. At that time, the blank will probably lie between points 2 and 3 or between points 3 and 4 of FIG. 1. In the former case, the increased pressure will cause the blank to more rapidly strain and quickly enter the zone between points 3 and 4. Regardless of whether the blank subsequently strains into the foregoing zone or is already there by the time point 4 is reached on the pressure versus time plot of FIG. 2, the increasing forming pressure results in a drastically increased strain rate in this zone. The differential between the applied pressure and the pressure required to maintain the desired constant strain rate increases, and with it the strain rate, until either rupture occurs or the blank touches the bottom of the die cavity and the required pressure begins to increase.
A further drawback inherent to the use of a pressure versus time plot is that if the forming must be stopped for any reason, such as a malfunction of equipment, it is not possible to determine how much further forming will have progressed while the pressure was held constant, or even reduced, during the interruption. Continuing the forming cycle after an interruption thus increases the risk of rupture.
Efforts have been made to monitor the deformation of the blank so that the pressure can be adjusted to take into account deviation of the actual position of the forming blank from the predicted position, and avoid rupture due to this problem. For example, in U.S. Pat. No. 4,489,579 Daime et al show a hollow tube slideably projecting into the die cavity and having one end in contact with the blank in order to measure the distortion of the blank. Electrical monitoring devices are situated at each recess angle of the die cavity to inform of the arrival of the blank. Further, Japanese Patent No. 1-210130 issued to Hisada shows a touch sensor slideably projecting into the die cavity. The sensor comes into contact at only one point on the blank, and thus would not be able to indicate how the blank is forming in corners or other recesses in the die cavity.
Both of the foregoing approaches require breaching the die cavity, and thus add mechanical complexity and expense to the forming die. Furthermore, both require having a sensor in contact with the forming blank. This will result in the area of the blank in contact with the sensor being prevented from forming normally, thus affecting the strain rate and causing a discontinuity in material thickness in the formed object between the area that was in contact with the sensor and the adjacent area.
In U.S. Pat. No. 5,007,265 Mahoney et al use a video camera to view reference marks on the blank and thereby monitor its strain. The device described therein thus requires a special forming die having a window to allow observation of the forming blank. Such a special forming die would clearly be more expensive to fabricate than a conventional forming die. A further drawback is that the blank must be continually observed by the operator during the forming process, and therefore the use of the described apparatus does not lend itself to automation.
Computer programs have been created to predict the progress of the superplastic forming of a blank. However, the accuracy of these programs is no better than the accuracy of the input data of the original thickness of the blank and the slippage of the blank after it comes into contact with the surface of the die cavity. Further error is introduced by the failure of these programs to compensate for the effect on strain rate and thickness caused by variations in the temperature from point to point over the blank, in addition to changes in the temperature that inevitably occur with time throughout the forming cycle.
Another approach to controlling superplastic forming is shown by Yasui in U.S. patent application Ser. No. 636,791, now U.S. Pat. No. 5,129,248. Yasui is also the inventor of the present invention. The foregoing application is assigned to the same assignee as the present application. The aforementioned application shows controlling the rate of forming by measuring and regulating the flow rate of gas mass into the forming die. The apparatus and method shown therein present an advance over controlling forming by regulating pressure according to a plot of pressure versus time because they do not rely on the assumption that an empirically determined strain rate remains constant during the forming process and over the entire forming blank. The possibility of rupture inherent to the use of the pressure versus time plot is thus avoided for the reasons previously discussed herein.
In U.S. Pat. No. 4,708,008 Yasui et al show an apparatus for controlling the superplastic forming of a blank by continuously monitoring the height of liquid in a manometer fluidly communicating with the gas being displaced and exhausted from a forming die cavity during forming, and by regulating the forming pressure responsive to the height of the liquid in the manometer. Yasui is also the inventor of the present invention, and the foregoing patent is assigned to the same assignee as the present application.
Before forming is begun, the use of the aforementioned device requires an empirical or mathematical analysis to determine the relationship between the forming pressure and the location of the blank as it is forming. The relationship between the location of the blank and the displaced volume of the exhaust gas is then determined. The displaced volume is then converted into exhaust pressure, and the exhaust pressure is converted into the height of liquid in a manometer fluidly communicating with the exhaust gas. The foregoing relationships are used to derive the relationship between forming pressure and the height of liquid in the manometer, which is the relationship used to guide the forming process. The foregoing analyses are complex even for formed objects having the simplest of shapes.